I hope this website will become a valuable resource for everyone learning and doing linear algebra. Here are key links:

Introduction to Linear Algebra, 5th Edition (2016 edition) Introduction to Linear Algebra, 6th Edition (2023 edition) Accessibility

Our recent textbook Linear Algebra for Everyone starts with the idea of independent columns This leads to a factorization A = CR where C contains those independent columns from A

Textbooks, Websites, and Video Lectures Part 1 : Basic Ideas of Linear Algebra 1.1 Linear Combinations of Vectors 1.2 Dot Products v · w and Lengths || v || and Angles θ 1.3 Matrices …

Our recent textbook Linear Algebra for Everyone starts with the idea of independent columns This leads to a factorization A = CR where C contains those independent columns from A

Linear combinations can fill all of space, or only a plane. We need a picture to show the crucial difference between u, v, w (the first example) and u, v, w∗ (all in the same plane).

I am happy for you to see this Fifth Edition of Introduction to Linear Algebra. This is the text for my video lectures on MIT’s OpenCourseWare (ocw.mit.edu and also YouTube).

18.06 and 18.06 SC Linear Algebra - The video lectures are on ocw.mit.edu and YouTube/mitocw. Many universities use the textbooks Introduction to Linear Algebra and Linear Algebra for Everyone.

You need to know about the video lectures for MIT’s Linear Algebra course Math 18.06. Those videos go with this book, and they are part of MIT’s OpenCourseWare.

Some linear combination of the 100 rows is the row of 100 zeros. Some linear combination of the 100 columns is the column of zeros. A very singular matrix has all ones: A = ones (100). A better …